Wireless audio audio-output devices, such as earbuds, headphones, or loudspeakers, may be used to communicate wirelessly with a user device, such as a smartphone, smartwatch, or similar device, and with each other. The wireless audio-output devices may be used to output audio sent from the user device, such as music, as part of two-way communications, such as telephone calls, and/or to receive audio for speech recognition. Speech-recognition systems have progressed to the point at which humans are able to interact with computing devices using their voices. Such systems employ techniques to detect when speech is occurring and to identify the words spoken by a human user based on the received audio input. Voice-activity detection, speech recognition, and natural-language understanding processing techniques enable speech-based user control of a computing device to perform tasks based on the user's spoken commands. The combination of voice-activity detection, speech recognition, and/or natural-language understanding processing techniques is referred to herein as speech processing. Speech processing may also involve converting a user's speech into text data, which may then be provided to various text-based software applications.